Mine would be a Jeopardy game starring Will Ferrel, Weird Al Yankovic and Sean Connery.
Mine would actually be a game that has a battle system remarkably similar to Tales of Symphonia's, a character progression remarkably similar to final fantasy tactics' and a story that's remarkably similar to any and all of the Phoenix Wright games.
You forgot Burt Reynolds...
Also mine would be a single-player game.
It would be an RPG and based on you, obviously the main character, customizable like most RPGs let you customize your character.
You were selected as a child based on genetics, to be part of a secret organization that has been running in secret since just before the rise of the Roman Empire. However the game would take place in modern day settings, that's just to let you know how old this organization is.
Anyway, this organization is secret, because the public does not know about it. However, members of the organization have high ranking positions in governments and military organizations throughout the world.
You, as an infant, selected because of genetics begin your training (similar to Spartans) and this organization trains these people to be the best in the world at everything. They learn many languages, many forms of martial arts, survival skills, memory skills, mind-control skills, which means you have control of your own mind, for example you can control your heart beat and have a near-infinite memory to help you learn many languages very quickly.
Not everyone who goes through this training is able to learn everything...only a few are, and many die. However you are one of those few people who become one of the best agents of this organization. Those who do not learn everything are still agents of the organization, just not the best. And not everyone is trained like this. Just those who pass the genetics test. Everyone else is trained and part of the organization, just specifically trained in a certain field.
Anyway, this organization, like I said before has people in high places all across the world and was also the real reason why America won the Revolutionary War. The organization took advantage of this and began planting seeds to be part of running the nation.
One of the top agents goes rouge, and these top agents are trained to be nearly invincible and you are assigned to track this agent down and kill him.
During this quest there will be many side quests...whatever you can think of. Basically you are one of the best spies or whatever you want in the world.
So yeah that would be a cool game IMO. Just thought of this all off the top of my head haha.